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On the number of lattice points in a ball

Jeffrey D Vaaler

Abstract

We prove a fairly general inequality that estimates the number of lattice points in a ball of positive radius in general position in a Euclidean space. The bound is uniform over lattices induced by a matrix having a bounded operator norm.

On the number of lattice points in a ball

Abstract

We prove a fairly general inequality that estimates the number of lattice points in a ball of positive radius in general position in a Euclidean space. The bound is uniform over lattices induced by a matrix having a bounded operator norm.
Paper Structure (5 sections, 139 equations)

This paper contains 5 sections, 139 equations.

Table of Contents

  1. Introduction
  2. Entire functions of exponential type
  3. Beurling-Selberg extremal problems
  4. The Poisson formula
  5. Proof of Theorem \ref{['thmintro1']}

Theorems & Definitions (6)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof